A Theoretical Model of Deformed Klein–Gordon Equation with Generalized Modified Screened Coulomb Plus Inversely Quadratic Yukawa Potential in RNCQM Symmetries

In this work, we present approximate and analytical solutions of the deformed Klein–Gordon containing an interaction of the equal vector and scalar potential newly generalized modified screened Coulomb plus inversely quadratic Yukawa potential. To overcome the centrifugal barrier, we employed the well-known Greene and Aldrich approximation scheme. This study is realized in the relativistic noncommutative 3-dimensional real space symmetries. This potential is suggested to compute bound-state normalizations and the energy levels of neutral atoms. Furthermore, it is considered a good potential in studying Hydrogen-like atoms. Both ordinary Bopp’s shift method, perturbation theory, and the Greene–Aldrich approximation method of handling centrifugal barriers are surveyed to get generalized excited states energy E r - n c sip V 0 , V 1 , k j , l , s , α , n , j , l , m , s , as a function of the shift energy, the energy of the modified screened Coulomb plus inversely quadratic Yukawa potential, the discreet atomic quantum numbers ( j , l , s , m ) , the potential parameters ( V 0 , V 1 , α ) and the infinitesimal noncommutativity parameters ( θ and σ ). We have shown that the degeneracy of the initial spectral under the potential in the relativistic commutative quantum mechanics RCQM is broken and replaced by newly degeneracy of energy levels; this gives more precisions in measurement and better off compared to results of ordinary RCQM.